Please can you help me with the three questions below. If you can do them, can you show your working/explanation please.

1.) If gravitational forces are so weak, how can they be responsible for the large-scale structure of the universe?

2.) The force between two 1kg spheres separated by 1m is tiny (given by G). Now scale up the system by a linear factor of 10^9. By what factor do each of the following increase:
a) the radius of each sphere
b) the volume of each sphere
c) the mass of each sphere (assuming density doesnt change)
d) the gravitational attraction between the spheres

How does this back up the answer to part 1?

3.) How would you expect a material which has negative mass to behave?

My answers:

1.) There is a lot of mass in the universe, including dark matter

I dont know how you can do 2 as there is no radius or volume in the law of gravitation equation.

3.) How would you expect a material which has negative mass to behave?

I would assume that instead of attracting other masses it will repel them. This is because gravitational force is negative (indicating attraction). If the mass is also negative than the force will be positive and this will indicate an increase in p.e, i.e. repulsion.

I dont know how you can do 2 as there is no radius or volume in the law of gravitation equation.

The equation for Gravitational force is F=-GM1M2/R2
The negative sign is often ignored. The centre of each sphere acts as the point where gravitational field is exerted from/upon. Thus R in the equation will be 1m + radius of sphere 1 & 2. The radius is related to the volume by: V=4/3piexr3

For question 1, you are dealing with non-charged bodies on a universal scale (Eg, Planets). As this is the case, Gravitational force is the only force which acts over a long distance. So it can be the only force which is responsible for the large scale structure of the universe.

For Q1, it's because only electromagnetism and gravity act of large distances, and EM doesn't factor into the large scale shape of the universe because it has both positive and negative charges, which cancel each other out on large scales. There is no such thing as negative gravity charge, so gravity just adds up more and more as you increase the mass.

(Original post by AlphaNumeric)
For Q1, it's because only electromagnetism and gravity act of large distances, and EM doesn't factor into the large scale shape of the universe because it has both positive and negative charges, which cancel each other out on large scales. There is no such thing as negative gravity charge, so gravity just adds up more and more as you increase the mass.

Ironically it is because the electric force is so strong that negative and positive charges stay so close together, thus canceling out their effect at long distances (the force from an electric dipole drops at a rate of inverse (4hypercube?) as opposed to inverse square law.). That and as Alpha said, that there exists a conservation of charge, but no conservation of mass law, no matter how many Chemists (they don't measure things accurately enough you see) say otherwise.